Properties

Label 1045.2.b.a.419.1
Level $1045$
Weight $2$
Character 1045.419
Analytic conductor $8.344$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1045,2,Mod(419,1045)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1045.419");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1045.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.34436701122\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 419.1
Root \(0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 1045.419
Dual form 1045.2.b.a.419.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.41421i q^{2} +2.00000i q^{3} -3.82843 q^{4} +(-1.00000 - 2.00000i) q^{5} +4.82843 q^{6} -4.82843i q^{7} +4.41421i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-2.41421i q^{2} +2.00000i q^{3} -3.82843 q^{4} +(-1.00000 - 2.00000i) q^{5} +4.82843 q^{6} -4.82843i q^{7} +4.41421i q^{8} -1.00000 q^{9} +(-4.82843 + 2.41421i) q^{10} -1.00000 q^{11} -7.65685i q^{12} +1.17157i q^{13} -11.6569 q^{14} +(4.00000 - 2.00000i) q^{15} +3.00000 q^{16} -1.17157i q^{17} +2.41421i q^{18} +1.00000 q^{19} +(3.82843 + 7.65685i) q^{20} +9.65685 q^{21} +2.41421i q^{22} -3.65685i q^{23} -8.82843 q^{24} +(-3.00000 + 4.00000i) q^{25} +2.82843 q^{26} +4.00000i q^{27} +18.4853i q^{28} -0.828427 q^{29} +(-4.82843 - 9.65685i) q^{30} -1.17157 q^{31} +1.58579i q^{32} -2.00000i q^{33} -2.82843 q^{34} +(-9.65685 + 4.82843i) q^{35} +3.82843 q^{36} -8.48528i q^{37} -2.41421i q^{38} -2.34315 q^{39} +(8.82843 - 4.41421i) q^{40} -10.4853 q^{41} -23.3137i q^{42} +4.82843i q^{43} +3.82843 q^{44} +(1.00000 + 2.00000i) q^{45} -8.82843 q^{46} -0.343146i q^{47} +6.00000i q^{48} -16.3137 q^{49} +(9.65685 + 7.24264i) q^{50} +2.34315 q^{51} -4.48528i q^{52} +5.17157i q^{53} +9.65685 q^{54} +(1.00000 + 2.00000i) q^{55} +21.3137 q^{56} +2.00000i q^{57} +2.00000i q^{58} -2.82843 q^{59} +(-15.3137 + 7.65685i) q^{60} -2.00000 q^{61} +2.82843i q^{62} +4.82843i q^{63} +9.82843 q^{64} +(2.34315 - 1.17157i) q^{65} -4.82843 q^{66} -6.00000i q^{67} +4.48528i q^{68} +7.31371 q^{69} +(11.6569 + 23.3137i) q^{70} -9.17157 q^{71} -4.41421i q^{72} +6.82843i q^{73} -20.4853 q^{74} +(-8.00000 - 6.00000i) q^{75} -3.82843 q^{76} +4.82843i q^{77} +5.65685i q^{78} +5.65685 q^{79} +(-3.00000 - 6.00000i) q^{80} -11.0000 q^{81} +25.3137i q^{82} +10.4853i q^{83} -36.9706 q^{84} +(-2.34315 + 1.17157i) q^{85} +11.6569 q^{86} -1.65685i q^{87} -4.41421i q^{88} +15.6569 q^{89} +(4.82843 - 2.41421i) q^{90} +5.65685 q^{91} +14.0000i q^{92} -2.34315i q^{93} -0.828427 q^{94} +(-1.00000 - 2.00000i) q^{95} -3.17157 q^{96} -6.82843i q^{97} +39.3848i q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{4} - 4 q^{5} + 8 q^{6} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{4} - 4 q^{5} + 8 q^{6} - 4 q^{9} - 8 q^{10} - 4 q^{11} - 24 q^{14} + 16 q^{15} + 12 q^{16} + 4 q^{19} + 4 q^{20} + 16 q^{21} - 24 q^{24} - 12 q^{25} + 8 q^{29} - 8 q^{30} - 16 q^{31} - 16 q^{35} + 4 q^{36} - 32 q^{39} + 24 q^{40} - 8 q^{41} + 4 q^{44} + 4 q^{45} - 24 q^{46} - 20 q^{49} + 16 q^{50} + 32 q^{51} + 16 q^{54} + 4 q^{55} + 40 q^{56} - 16 q^{60} - 8 q^{61} + 28 q^{64} + 32 q^{65} - 8 q^{66} - 16 q^{69} + 24 q^{70} - 48 q^{71} - 48 q^{74} - 32 q^{75} - 4 q^{76} - 12 q^{80} - 44 q^{81} - 80 q^{84} - 32 q^{85} + 24 q^{86} + 40 q^{89} + 8 q^{90} + 8 q^{94} - 4 q^{95} - 24 q^{96} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times\).

\(n\) \(496\) \(761\) \(837\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.41421i 1.70711i −0.521005 0.853553i \(-0.674443\pi\)
0.521005 0.853553i \(-0.325557\pi\)
\(3\) 2.00000i 1.15470i 0.816497 + 0.577350i \(0.195913\pi\)
−0.816497 + 0.577350i \(0.804087\pi\)
\(4\) −3.82843 −1.91421
\(5\) −1.00000 2.00000i −0.447214 0.894427i
\(6\) 4.82843 1.97120
\(7\) 4.82843i 1.82497i −0.409106 0.912487i \(-0.634159\pi\)
0.409106 0.912487i \(-0.365841\pi\)
\(8\) 4.41421i 1.56066i
\(9\) −1.00000 −0.333333
\(10\) −4.82843 + 2.41421i −1.52688 + 0.763441i
\(11\) −1.00000 −0.301511
\(12\) 7.65685i 2.21034i
\(13\) 1.17157i 0.324936i 0.986714 + 0.162468i \(0.0519454\pi\)
−0.986714 + 0.162468i \(0.948055\pi\)
\(14\) −11.6569 −3.11543
\(15\) 4.00000 2.00000i 1.03280 0.516398i
\(16\) 3.00000 0.750000
\(17\) 1.17157i 0.284148i −0.989856 0.142074i \(-0.954623\pi\)
0.989856 0.142074i \(-0.0453771\pi\)
\(18\) 2.41421i 0.569036i
\(19\) 1.00000 0.229416
\(20\) 3.82843 + 7.65685i 0.856062 + 1.71212i
\(21\) 9.65685 2.10730
\(22\) 2.41421i 0.514712i
\(23\) 3.65685i 0.762507i −0.924471 0.381253i \(-0.875493\pi\)
0.924471 0.381253i \(-0.124507\pi\)
\(24\) −8.82843 −1.80210
\(25\) −3.00000 + 4.00000i −0.600000 + 0.800000i
\(26\) 2.82843 0.554700
\(27\) 4.00000i 0.769800i
\(28\) 18.4853i 3.49339i
\(29\) −0.828427 −0.153835 −0.0769175 0.997037i \(-0.524508\pi\)
−0.0769175 + 0.997037i \(0.524508\pi\)
\(30\) −4.82843 9.65685i −0.881546 1.76309i
\(31\) −1.17157 −0.210421 −0.105210 0.994450i \(-0.533552\pi\)
−0.105210 + 0.994450i \(0.533552\pi\)
\(32\) 1.58579i 0.280330i
\(33\) 2.00000i 0.348155i
\(34\) −2.82843 −0.485071
\(35\) −9.65685 + 4.82843i −1.63231 + 0.816153i
\(36\) 3.82843 0.638071
\(37\) 8.48528i 1.39497i −0.716599 0.697486i \(-0.754302\pi\)
0.716599 0.697486i \(-0.245698\pi\)
\(38\) 2.41421i 0.391637i
\(39\) −2.34315 −0.375204
\(40\) 8.82843 4.41421i 1.39590 0.697948i
\(41\) −10.4853 −1.63753 −0.818763 0.574132i \(-0.805340\pi\)
−0.818763 + 0.574132i \(0.805340\pi\)
\(42\) 23.3137i 3.59738i
\(43\) 4.82843i 0.736328i 0.929761 + 0.368164i \(0.120014\pi\)
−0.929761 + 0.368164i \(0.879986\pi\)
\(44\) 3.82843 0.577157
\(45\) 1.00000 + 2.00000i 0.149071 + 0.298142i
\(46\) −8.82843 −1.30168
\(47\) 0.343146i 0.0500530i −0.999687 0.0250265i \(-0.992033\pi\)
0.999687 0.0250265i \(-0.00796701\pi\)
\(48\) 6.00000i 0.866025i
\(49\) −16.3137 −2.33053
\(50\) 9.65685 + 7.24264i 1.36569 + 1.02426i
\(51\) 2.34315 0.328106
\(52\) 4.48528i 0.621997i
\(53\) 5.17157i 0.710370i 0.934796 + 0.355185i \(0.115582\pi\)
−0.934796 + 0.355185i \(0.884418\pi\)
\(54\) 9.65685 1.31413
\(55\) 1.00000 + 2.00000i 0.134840 + 0.269680i
\(56\) 21.3137 2.84816
\(57\) 2.00000i 0.264906i
\(58\) 2.00000i 0.262613i
\(59\) −2.82843 −0.368230 −0.184115 0.982905i \(-0.558942\pi\)
−0.184115 + 0.982905i \(0.558942\pi\)
\(60\) −15.3137 + 7.65685i −1.97699 + 0.988496i
\(61\) −2.00000 −0.256074 −0.128037 0.991769i \(-0.540868\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) 2.82843i 0.359211i
\(63\) 4.82843i 0.608325i
\(64\) 9.82843 1.22855
\(65\) 2.34315 1.17157i 0.290631 0.145316i
\(66\) −4.82843 −0.594338
\(67\) 6.00000i 0.733017i −0.930415 0.366508i \(-0.880553\pi\)
0.930415 0.366508i \(-0.119447\pi\)
\(68\) 4.48528i 0.543920i
\(69\) 7.31371 0.880467
\(70\) 11.6569 + 23.3137i 1.39326 + 2.78652i
\(71\) −9.17157 −1.08847 −0.544233 0.838934i \(-0.683179\pi\)
−0.544233 + 0.838934i \(0.683179\pi\)
\(72\) 4.41421i 0.520220i
\(73\) 6.82843i 0.799207i 0.916688 + 0.399603i \(0.130852\pi\)
−0.916688 + 0.399603i \(0.869148\pi\)
\(74\) −20.4853 −2.38137
\(75\) −8.00000 6.00000i −0.923760 0.692820i
\(76\) −3.82843 −0.439151
\(77\) 4.82843i 0.550250i
\(78\) 5.65685i 0.640513i
\(79\) 5.65685 0.636446 0.318223 0.948016i \(-0.396914\pi\)
0.318223 + 0.948016i \(0.396914\pi\)
\(80\) −3.00000 6.00000i −0.335410 0.670820i
\(81\) −11.0000 −1.22222
\(82\) 25.3137i 2.79543i
\(83\) 10.4853i 1.15091i 0.817834 + 0.575455i \(0.195175\pi\)
−0.817834 + 0.575455i \(0.804825\pi\)
\(84\) −36.9706 −4.03382
\(85\) −2.34315 + 1.17157i −0.254150 + 0.127075i
\(86\) 11.6569 1.25699
\(87\) 1.65685i 0.177633i
\(88\) 4.41421i 0.470557i
\(89\) 15.6569 1.65962 0.829812 0.558044i \(-0.188448\pi\)
0.829812 + 0.558044i \(0.188448\pi\)
\(90\) 4.82843 2.41421i 0.508961 0.254480i
\(91\) 5.65685 0.592999
\(92\) 14.0000i 1.45960i
\(93\) 2.34315i 0.242973i
\(94\) −0.828427 −0.0854457
\(95\) −1.00000 2.00000i −0.102598 0.205196i
\(96\) −3.17157 −0.323697
\(97\) 6.82843i 0.693322i −0.937991 0.346661i \(-0.887315\pi\)
0.937991 0.346661i \(-0.112685\pi\)
\(98\) 39.3848i 3.97846i
\(99\) 1.00000 0.100504
\(100\) 11.4853 15.3137i 1.14853 1.53137i
\(101\) −13.3137 −1.32476 −0.662382 0.749166i \(-0.730454\pi\)
−0.662382 + 0.749166i \(0.730454\pi\)
\(102\) 5.65685i 0.560112i
\(103\) 15.6569i 1.54272i −0.636402 0.771358i \(-0.719578\pi\)
0.636402 0.771358i \(-0.280422\pi\)
\(104\) −5.17157 −0.507114
\(105\) −9.65685 19.3137i −0.942412 1.88482i
\(106\) 12.4853 1.21268
\(107\) 14.9706i 1.44726i 0.690189 + 0.723629i \(0.257528\pi\)
−0.690189 + 0.723629i \(0.742472\pi\)
\(108\) 15.3137i 1.47356i
\(109\) 4.82843 0.462479 0.231240 0.972897i \(-0.425722\pi\)
0.231240 + 0.972897i \(0.425722\pi\)
\(110\) 4.82843 2.41421i 0.460372 0.230186i
\(111\) 16.9706 1.61077
\(112\) 14.4853i 1.36873i
\(113\) 18.1421i 1.70667i −0.521364 0.853334i \(-0.674577\pi\)
0.521364 0.853334i \(-0.325423\pi\)
\(114\) 4.82843 0.452224
\(115\) −7.31371 + 3.65685i −0.682007 + 0.341003i
\(116\) 3.17157 0.294473
\(117\) 1.17157i 0.108312i
\(118\) 6.82843i 0.628608i
\(119\) −5.65685 −0.518563
\(120\) 8.82843 + 17.6569i 0.805921 + 1.61184i
\(121\) 1.00000 0.0909091
\(122\) 4.82843i 0.437145i
\(123\) 20.9706i 1.89085i
\(124\) 4.48528 0.402790
\(125\) 11.0000 + 2.00000i 0.983870 + 0.178885i
\(126\) 11.6569 1.03848
\(127\) 14.0000i 1.24230i −0.783692 0.621150i \(-0.786666\pi\)
0.783692 0.621150i \(-0.213334\pi\)
\(128\) 20.5563i 1.81694i
\(129\) −9.65685 −0.850239
\(130\) −2.82843 5.65685i −0.248069 0.496139i
\(131\) −15.3137 −1.33796 −0.668982 0.743278i \(-0.733270\pi\)
−0.668982 + 0.743278i \(0.733270\pi\)
\(132\) 7.65685i 0.666444i
\(133\) 4.82843i 0.418678i
\(134\) −14.4853 −1.25134
\(135\) 8.00000 4.00000i 0.688530 0.344265i
\(136\) 5.17157 0.443459
\(137\) 8.00000i 0.683486i −0.939793 0.341743i \(-0.888983\pi\)
0.939793 0.341743i \(-0.111017\pi\)
\(138\) 17.6569i 1.50305i
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 36.9706 18.4853i 3.12458 1.56229i
\(141\) 0.686292 0.0577962
\(142\) 22.1421i 1.85813i
\(143\) 1.17157i 0.0979718i
\(144\) −3.00000 −0.250000
\(145\) 0.828427 + 1.65685i 0.0687971 + 0.137594i
\(146\) 16.4853 1.36433
\(147\) 32.6274i 2.69106i
\(148\) 32.4853i 2.67027i
\(149\) 19.6569 1.61035 0.805176 0.593036i \(-0.202071\pi\)
0.805176 + 0.593036i \(0.202071\pi\)
\(150\) −14.4853 + 19.3137i −1.18272 + 1.57696i
\(151\) 21.6569 1.76241 0.881205 0.472735i \(-0.156733\pi\)
0.881205 + 0.472735i \(0.156733\pi\)
\(152\) 4.41421i 0.358040i
\(153\) 1.17157i 0.0947161i
\(154\) 11.6569 0.939336
\(155\) 1.17157 + 2.34315i 0.0941030 + 0.188206i
\(156\) 8.97056 0.718220
\(157\) 12.0000i 0.957704i −0.877896 0.478852i \(-0.841053\pi\)
0.877896 0.478852i \(-0.158947\pi\)
\(158\) 13.6569i 1.08648i
\(159\) −10.3431 −0.820265
\(160\) 3.17157 1.58579i 0.250735 0.125367i
\(161\) −17.6569 −1.39156
\(162\) 26.5563i 2.08646i
\(163\) 2.00000i 0.156652i −0.996928 0.0783260i \(-0.975042\pi\)
0.996928 0.0783260i \(-0.0249575\pi\)
\(164\) 40.1421 3.13457
\(165\) −4.00000 + 2.00000i −0.311400 + 0.155700i
\(166\) 25.3137 1.96472
\(167\) 19.6569i 1.52109i −0.649283 0.760547i \(-0.724931\pi\)
0.649283 0.760547i \(-0.275069\pi\)
\(168\) 42.6274i 3.28878i
\(169\) 11.6274 0.894417
\(170\) 2.82843 + 5.65685i 0.216930 + 0.433861i
\(171\) −1.00000 −0.0764719
\(172\) 18.4853i 1.40949i
\(173\) 4.48528i 0.341010i −0.985357 0.170505i \(-0.945460\pi\)
0.985357 0.170505i \(-0.0545398\pi\)
\(174\) −4.00000 −0.303239
\(175\) 19.3137 + 14.4853i 1.45998 + 1.09498i
\(176\) −3.00000 −0.226134
\(177\) 5.65685i 0.425195i
\(178\) 37.7990i 2.83315i
\(179\) 0.485281 0.0362716 0.0181358 0.999836i \(-0.494227\pi\)
0.0181358 + 0.999836i \(0.494227\pi\)
\(180\) −3.82843 7.65685i −0.285354 0.570708i
\(181\) 14.0000 1.04061 0.520306 0.853980i \(-0.325818\pi\)
0.520306 + 0.853980i \(0.325818\pi\)
\(182\) 13.6569i 1.01231i
\(183\) 4.00000i 0.295689i
\(184\) 16.1421 1.19001
\(185\) −16.9706 + 8.48528i −1.24770 + 0.623850i
\(186\) −5.65685 −0.414781
\(187\) 1.17157i 0.0856739i
\(188\) 1.31371i 0.0958120i
\(189\) 19.3137 1.40487
\(190\) −4.82843 + 2.41421i −0.350291 + 0.175145i
\(191\) −16.9706 −1.22795 −0.613973 0.789327i \(-0.710430\pi\)
−0.613973 + 0.789327i \(0.710430\pi\)
\(192\) 19.6569i 1.41861i
\(193\) 14.1421i 1.01797i 0.860774 + 0.508987i \(0.169980\pi\)
−0.860774 + 0.508987i \(0.830020\pi\)
\(194\) −16.4853 −1.18357
\(195\) 2.34315 + 4.68629i 0.167796 + 0.335592i
\(196\) 62.4558 4.46113
\(197\) 22.1421i 1.57756i −0.614674 0.788781i \(-0.710713\pi\)
0.614674 0.788781i \(-0.289287\pi\)
\(198\) 2.41421i 0.171571i
\(199\) −5.65685 −0.401004 −0.200502 0.979693i \(-0.564257\pi\)
−0.200502 + 0.979693i \(0.564257\pi\)
\(200\) −17.6569 13.2426i −1.24853 0.936396i
\(201\) 12.0000 0.846415
\(202\) 32.1421i 2.26151i
\(203\) 4.00000i 0.280745i
\(204\) −8.97056 −0.628065
\(205\) 10.4853 + 20.9706i 0.732324 + 1.46465i
\(206\) −37.7990 −2.63358
\(207\) 3.65685i 0.254169i
\(208\) 3.51472i 0.243702i
\(209\) −1.00000 −0.0691714
\(210\) −46.6274 + 23.3137i −3.21760 + 1.60880i
\(211\) −7.31371 −0.503496 −0.251748 0.967793i \(-0.581005\pi\)
−0.251748 + 0.967793i \(0.581005\pi\)
\(212\) 19.7990i 1.35980i
\(213\) 18.3431i 1.25685i
\(214\) 36.1421 2.47063
\(215\) 9.65685 4.82843i 0.658592 0.329296i
\(216\) −17.6569 −1.20140
\(217\) 5.65685i 0.384012i
\(218\) 11.6569i 0.789502i
\(219\) −13.6569 −0.922845
\(220\) −3.82843 7.65685i −0.258113 0.516225i
\(221\) 1.37258 0.0923299
\(222\) 40.9706i 2.74976i
\(223\) 0.343146i 0.0229787i 0.999934 + 0.0114894i \(0.00365726\pi\)
−0.999934 + 0.0114894i \(0.996343\pi\)
\(224\) 7.65685 0.511595
\(225\) 3.00000 4.00000i 0.200000 0.266667i
\(226\) −43.7990 −2.91347
\(227\) 23.6569i 1.57016i −0.619394 0.785080i \(-0.712622\pi\)
0.619394 0.785080i \(-0.287378\pi\)
\(228\) 7.65685i 0.507088i
\(229\) 22.0000 1.45380 0.726900 0.686743i \(-0.240960\pi\)
0.726900 + 0.686743i \(0.240960\pi\)
\(230\) 8.82843 + 17.6569i 0.582129 + 1.16426i
\(231\) −9.65685 −0.635374
\(232\) 3.65685i 0.240084i
\(233\) 12.4853i 0.817938i 0.912548 + 0.408969i \(0.134112\pi\)
−0.912548 + 0.408969i \(0.865888\pi\)
\(234\) −2.82843 −0.184900
\(235\) −0.686292 + 0.343146i −0.0447687 + 0.0223844i
\(236\) 10.8284 0.704871
\(237\) 11.3137i 0.734904i
\(238\) 13.6569i 0.885242i
\(239\) −27.3137 −1.76678 −0.883388 0.468641i \(-0.844744\pi\)
−0.883388 + 0.468641i \(0.844744\pi\)
\(240\) 12.0000 6.00000i 0.774597 0.387298i
\(241\) −10.4853 −0.675416 −0.337708 0.941251i \(-0.609652\pi\)
−0.337708 + 0.941251i \(0.609652\pi\)
\(242\) 2.41421i 0.155192i
\(243\) 10.0000i 0.641500i
\(244\) 7.65685 0.490180
\(245\) 16.3137 + 32.6274i 1.04224 + 2.08449i
\(246\) −50.6274 −3.22789
\(247\) 1.17157i 0.0745454i
\(248\) 5.17157i 0.328395i
\(249\) −20.9706 −1.32896
\(250\) 4.82843 26.5563i 0.305377 1.67957i
\(251\) −4.00000 −0.252478 −0.126239 0.992000i \(-0.540291\pi\)
−0.126239 + 0.992000i \(0.540291\pi\)
\(252\) 18.4853i 1.16446i
\(253\) 3.65685i 0.229904i
\(254\) −33.7990 −2.12074
\(255\) −2.34315 4.68629i −0.146733 0.293467i
\(256\) −29.9706 −1.87316
\(257\) 10.1421i 0.632649i −0.948651 0.316325i \(-0.897551\pi\)
0.948651 0.316325i \(-0.102449\pi\)
\(258\) 23.3137i 1.45145i
\(259\) −40.9706 −2.54579
\(260\) −8.97056 + 4.48528i −0.556331 + 0.278165i
\(261\) 0.828427 0.0512784
\(262\) 36.9706i 2.28405i
\(263\) 1.51472i 0.0934016i −0.998909 0.0467008i \(-0.985129\pi\)
0.998909 0.0467008i \(-0.0148707\pi\)
\(264\) 8.82843 0.543352
\(265\) 10.3431 5.17157i 0.635374 0.317687i
\(266\) −11.6569 −0.714728
\(267\) 31.3137i 1.91637i
\(268\) 22.9706i 1.40315i
\(269\) −10.9706 −0.668887 −0.334444 0.942416i \(-0.608548\pi\)
−0.334444 + 0.942416i \(0.608548\pi\)
\(270\) −9.65685 19.3137i −0.587697 1.17539i
\(271\) −11.3137 −0.687259 −0.343629 0.939105i \(-0.611656\pi\)
−0.343629 + 0.939105i \(0.611656\pi\)
\(272\) 3.51472i 0.213111i
\(273\) 11.3137i 0.684737i
\(274\) −19.3137 −1.16678
\(275\) 3.00000 4.00000i 0.180907 0.241209i
\(276\) −28.0000 −1.68540
\(277\) 13.1716i 0.791403i 0.918379 + 0.395702i \(0.129499\pi\)
−0.918379 + 0.395702i \(0.870501\pi\)
\(278\) 9.65685i 0.579180i
\(279\) 1.17157 0.0701402
\(280\) −21.3137 42.6274i −1.27374 2.54748i
\(281\) 31.4558 1.87650 0.938249 0.345960i \(-0.112447\pi\)
0.938249 + 0.345960i \(0.112447\pi\)
\(282\) 1.65685i 0.0986642i
\(283\) 10.4853i 0.623285i 0.950199 + 0.311643i \(0.100879\pi\)
−0.950199 + 0.311643i \(0.899121\pi\)
\(284\) 35.1127 2.08356
\(285\) 4.00000 2.00000i 0.236940 0.118470i
\(286\) −2.82843 −0.167248
\(287\) 50.6274i 2.98844i
\(288\) 1.58579i 0.0934434i
\(289\) 15.6274 0.919260
\(290\) 4.00000 2.00000i 0.234888 0.117444i
\(291\) 13.6569 0.800579
\(292\) 26.1421i 1.52985i
\(293\) 2.14214i 0.125145i 0.998040 + 0.0625724i \(0.0199304\pi\)
−0.998040 + 0.0625724i \(0.980070\pi\)
\(294\) −78.7696 −4.59393
\(295\) 2.82843 + 5.65685i 0.164677 + 0.329355i
\(296\) 37.4558 2.17708
\(297\) 4.00000i 0.232104i
\(298\) 47.4558i 2.74904i
\(299\) 4.28427 0.247766
\(300\) 30.6274 + 22.9706i 1.76827 + 1.32621i
\(301\) 23.3137 1.34378
\(302\) 52.2843i 3.00862i
\(303\) 26.6274i 1.52971i
\(304\) 3.00000 0.172062
\(305\) 2.00000 + 4.00000i 0.114520 + 0.229039i
\(306\) 2.82843 0.161690
\(307\) 6.97056i 0.397831i 0.980017 + 0.198916i \(0.0637419\pi\)
−0.980017 + 0.198916i \(0.936258\pi\)
\(308\) 18.4853i 1.05330i
\(309\) 31.3137 1.78137
\(310\) 5.65685 2.82843i 0.321288 0.160644i
\(311\) −32.9706 −1.86959 −0.934795 0.355189i \(-0.884417\pi\)
−0.934795 + 0.355189i \(0.884417\pi\)
\(312\) 10.3431i 0.585565i
\(313\) 16.9706i 0.959233i −0.877478 0.479616i \(-0.840776\pi\)
0.877478 0.479616i \(-0.159224\pi\)
\(314\) −28.9706 −1.63490
\(315\) 9.65685 4.82843i 0.544102 0.272051i
\(316\) −21.6569 −1.21829
\(317\) 22.1421i 1.24363i −0.783166 0.621813i \(-0.786396\pi\)
0.783166 0.621813i \(-0.213604\pi\)
\(318\) 24.9706i 1.40028i
\(319\) 0.828427 0.0463830
\(320\) −9.82843 19.6569i −0.549426 1.09885i
\(321\) −29.9411 −1.67115
\(322\) 42.6274i 2.37553i
\(323\) 1.17157i 0.0651881i
\(324\) 42.1127 2.33959
\(325\) −4.68629 3.51472i −0.259949 0.194962i
\(326\) −4.82843 −0.267422
\(327\) 9.65685i 0.534025i
\(328\) 46.2843i 2.55562i
\(329\) −1.65685 −0.0913453
\(330\) 4.82843 + 9.65685i 0.265796 + 0.531592i
\(331\) 22.1421 1.21704 0.608521 0.793538i \(-0.291763\pi\)
0.608521 + 0.793538i \(0.291763\pi\)
\(332\) 40.1421i 2.20309i
\(333\) 8.48528i 0.464991i
\(334\) −47.4558 −2.59667
\(335\) −12.0000 + 6.00000i −0.655630 + 0.327815i
\(336\) 28.9706 1.58047
\(337\) 2.82843i 0.154074i 0.997028 + 0.0770371i \(0.0245460\pi\)
−0.997028 + 0.0770371i \(0.975454\pi\)
\(338\) 28.0711i 1.52686i
\(339\) 36.2843 1.97069
\(340\) 8.97056 4.48528i 0.486497 0.243249i
\(341\) 1.17157 0.0634442
\(342\) 2.41421i 0.130546i
\(343\) 44.9706i 2.42818i
\(344\) −21.3137 −1.14916
\(345\) −7.31371 14.6274i −0.393757 0.787514i
\(346\) −10.8284 −0.582140
\(347\) 19.1716i 1.02918i −0.857435 0.514592i \(-0.827943\pi\)
0.857435 0.514592i \(-0.172057\pi\)
\(348\) 6.34315i 0.340028i
\(349\) 16.3431 0.874829 0.437414 0.899260i \(-0.355894\pi\)
0.437414 + 0.899260i \(0.355894\pi\)
\(350\) 34.9706 46.6274i 1.86926 2.49234i
\(351\) −4.68629 −0.250136
\(352\) 1.58579i 0.0845227i
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) −13.6569 −0.725854
\(355\) 9.17157 + 18.3431i 0.486777 + 0.973553i
\(356\) −59.9411 −3.17687
\(357\) 11.3137i 0.598785i
\(358\) 1.17157i 0.0619196i
\(359\) 16.9706 0.895672 0.447836 0.894116i \(-0.352195\pi\)
0.447836 + 0.894116i \(0.352195\pi\)
\(360\) −8.82843 + 4.41421i −0.465299 + 0.232649i
\(361\) 1.00000 0.0526316
\(362\) 33.7990i 1.77644i
\(363\) 2.00000i 0.104973i
\(364\) −21.6569 −1.13513
\(365\) 13.6569 6.82843i 0.714832 0.357416i
\(366\) −9.65685 −0.504772
\(367\) 31.6569i 1.65247i 0.563322 + 0.826237i \(0.309523\pi\)
−0.563322 + 0.826237i \(0.690477\pi\)
\(368\) 10.9706i 0.571880i
\(369\) 10.4853 0.545842
\(370\) 20.4853 + 40.9706i 1.06498 + 2.12996i
\(371\) 24.9706 1.29641
\(372\) 8.97056i 0.465102i
\(373\) 22.8284i 1.18201i −0.806667 0.591006i \(-0.798731\pi\)
0.806667 0.591006i \(-0.201269\pi\)
\(374\) 2.82843 0.146254
\(375\) −4.00000 + 22.0000i −0.206559 + 1.13608i
\(376\) 1.51472 0.0781156
\(377\) 0.970563i 0.0499865i
\(378\) 46.6274i 2.39826i
\(379\) −5.17157 −0.265646 −0.132823 0.991140i \(-0.542404\pi\)
−0.132823 + 0.991140i \(0.542404\pi\)
\(380\) 3.82843 + 7.65685i 0.196394 + 0.392788i
\(381\) 28.0000 1.43448
\(382\) 40.9706i 2.09624i
\(383\) 6.97056i 0.356179i 0.984014 + 0.178090i \(0.0569917\pi\)
−0.984014 + 0.178090i \(0.943008\pi\)
\(384\) 41.1127 2.09802
\(385\) 9.65685 4.82843i 0.492159 0.246079i
\(386\) 34.1421 1.73779
\(387\) 4.82843i 0.245443i
\(388\) 26.1421i 1.32717i
\(389\) 9.31371 0.472224 0.236112 0.971726i \(-0.424127\pi\)
0.236112 + 0.971726i \(0.424127\pi\)
\(390\) 11.3137 5.65685i 0.572892 0.286446i
\(391\) −4.28427 −0.216665
\(392\) 72.0122i 3.63717i
\(393\) 30.6274i 1.54495i
\(394\) −53.4558 −2.69307
\(395\) −5.65685 11.3137i −0.284627 0.569254i
\(396\) −3.82843 −0.192386
\(397\) 15.3137i 0.768573i 0.923214 + 0.384286i \(0.125553\pi\)
−0.923214 + 0.384286i \(0.874447\pi\)
\(398\) 13.6569i 0.684556i
\(399\) 9.65685 0.483447
\(400\) −9.00000 + 12.0000i −0.450000 + 0.600000i
\(401\) −17.3137 −0.864605 −0.432303 0.901729i \(-0.642299\pi\)
−0.432303 + 0.901729i \(0.642299\pi\)
\(402\) 28.9706i 1.44492i
\(403\) 1.37258i 0.0683732i
\(404\) 50.9706 2.53588
\(405\) 11.0000 + 22.0000i 0.546594 + 1.09319i
\(406\) 9.65685 0.479262
\(407\) 8.48528i 0.420600i
\(408\) 10.3431i 0.512062i
\(409\) 19.1716 0.947973 0.473987 0.880532i \(-0.342814\pi\)
0.473987 + 0.880532i \(0.342814\pi\)
\(410\) 50.6274 25.3137i 2.50031 1.25015i
\(411\) 16.0000 0.789222
\(412\) 59.9411i 2.95309i
\(413\) 13.6569i 0.672010i
\(414\) 8.82843 0.433894
\(415\) 20.9706 10.4853i 1.02940 0.514702i
\(416\) −1.85786 −0.0910893
\(417\) 8.00000i 0.391762i
\(418\) 2.41421i 0.118083i
\(419\) −12.9706 −0.633653 −0.316827 0.948483i \(-0.602617\pi\)
−0.316827 + 0.948483i \(0.602617\pi\)
\(420\) 36.9706 + 73.9411i 1.80398 + 3.60796i
\(421\) 6.97056 0.339724 0.169862 0.985468i \(-0.445668\pi\)
0.169862 + 0.985468i \(0.445668\pi\)
\(422\) 17.6569i 0.859522i
\(423\) 0.343146i 0.0166843i
\(424\) −22.8284 −1.10865
\(425\) 4.68629 + 3.51472i 0.227319 + 0.170489i
\(426\) −44.2843 −2.14558
\(427\) 9.65685i 0.467328i
\(428\) 57.3137i 2.77036i
\(429\) 2.34315 0.113128
\(430\) −11.6569 23.3137i −0.562143 1.12429i
\(431\) −38.6274 −1.86062 −0.930309 0.366778i \(-0.880461\pi\)
−0.930309 + 0.366778i \(0.880461\pi\)
\(432\) 12.0000i 0.577350i
\(433\) 6.82843i 0.328153i 0.986448 + 0.164077i \(0.0524644\pi\)
−0.986448 + 0.164077i \(0.947536\pi\)
\(434\) 13.6569 0.655550
\(435\) −3.31371 + 1.65685i −0.158880 + 0.0794401i
\(436\) −18.4853 −0.885284
\(437\) 3.65685i 0.174931i
\(438\) 32.9706i 1.57539i
\(439\) −29.6569 −1.41544 −0.707722 0.706491i \(-0.750277\pi\)
−0.707722 + 0.706491i \(0.750277\pi\)
\(440\) −8.82843 + 4.41421i −0.420879 + 0.210439i
\(441\) 16.3137 0.776843
\(442\) 3.31371i 0.157617i
\(443\) 13.3137i 0.632553i −0.948667 0.316277i \(-0.897567\pi\)
0.948667 0.316277i \(-0.102433\pi\)
\(444\) −64.9706 −3.08337
\(445\) −15.6569 31.3137i −0.742206 1.48441i
\(446\) 0.828427 0.0392272
\(447\) 39.3137i 1.85947i
\(448\) 47.4558i 2.24208i
\(449\) −30.9706 −1.46159 −0.730796 0.682596i \(-0.760851\pi\)
−0.730796 + 0.682596i \(0.760851\pi\)
\(450\) −9.65685 7.24264i −0.455228 0.341421i
\(451\) 10.4853 0.493733
\(452\) 69.4558i 3.26693i
\(453\) 43.3137i 2.03506i
\(454\) −57.1127 −2.68043
\(455\) −5.65685 11.3137i −0.265197 0.530395i
\(456\) −8.82843 −0.413429
\(457\) 23.7990i 1.11327i −0.830757 0.556635i \(-0.812092\pi\)
0.830757 0.556635i \(-0.187908\pi\)
\(458\) 53.1127i 2.48179i
\(459\) 4.68629 0.218737
\(460\) 28.0000 14.0000i 1.30551 0.652753i
\(461\) 34.2843 1.59678 0.798389 0.602142i \(-0.205686\pi\)
0.798389 + 0.602142i \(0.205686\pi\)
\(462\) 23.3137i 1.08465i
\(463\) 26.2843i 1.22153i −0.791811 0.610767i \(-0.790861\pi\)
0.791811 0.610767i \(-0.209139\pi\)
\(464\) −2.48528 −0.115376
\(465\) −4.68629 + 2.34315i −0.217322 + 0.108661i
\(466\) 30.1421 1.39631
\(467\) 15.6569i 0.724513i −0.932078 0.362256i \(-0.882006\pi\)
0.932078 0.362256i \(-0.117994\pi\)
\(468\) 4.48528i 0.207332i
\(469\) −28.9706 −1.33774
\(470\) 0.828427 + 1.65685i 0.0382125 + 0.0764250i
\(471\) 24.0000 1.10586
\(472\) 12.4853i 0.574682i
\(473\) 4.82843i 0.222011i
\(474\) 27.3137 1.25456
\(475\) −3.00000 + 4.00000i −0.137649 + 0.183533i
\(476\) 21.6569 0.992640
\(477\) 5.17157i 0.236790i
\(478\) 65.9411i 3.01608i
\(479\) −19.3137 −0.882466 −0.441233 0.897393i \(-0.645459\pi\)
−0.441233 + 0.897393i \(0.645459\pi\)
\(480\) 3.17157 + 6.34315i 0.144762 + 0.289524i
\(481\) 9.94113 0.453276
\(482\) 25.3137i 1.15301i
\(483\) 35.3137i 1.60683i
\(484\) −3.82843 −0.174019
\(485\) −13.6569 + 6.82843i −0.620126 + 0.310063i
\(486\) −24.1421 −1.09511
\(487\) 4.34315i 0.196807i −0.995147 0.0984034i \(-0.968626\pi\)
0.995147 0.0984034i \(-0.0313735\pi\)
\(488\) 8.82843i 0.399644i
\(489\) 4.00000 0.180886
\(490\) 78.7696 39.3848i 3.55845 1.77922i
\(491\) −3.02944 −0.136717 −0.0683583 0.997661i \(-0.521776\pi\)
−0.0683583 + 0.997661i \(0.521776\pi\)
\(492\) 80.2843i 3.61949i
\(493\) 0.970563i 0.0437119i
\(494\) 2.82843 0.127257
\(495\) −1.00000 2.00000i −0.0449467 0.0898933i
\(496\) −3.51472 −0.157816
\(497\) 44.2843i 1.98642i
\(498\) 50.6274i 2.26867i
\(499\) −23.3137 −1.04366 −0.521832 0.853048i \(-0.674751\pi\)
−0.521832 + 0.853048i \(0.674751\pi\)
\(500\) −42.1127 7.65685i −1.88334 0.342425i
\(501\) 39.3137 1.75641
\(502\) 9.65685i 0.431006i
\(503\) 2.20101i 0.0981382i 0.998795 + 0.0490691i \(0.0156255\pi\)
−0.998795 + 0.0490691i \(0.984375\pi\)
\(504\) −21.3137 −0.949388
\(505\) 13.3137 + 26.6274i 0.592452 + 1.18490i
\(506\) 8.82843 0.392471
\(507\) 23.2548i 1.03278i
\(508\) 53.5980i 2.37803i
\(509\) −20.3431 −0.901694 −0.450847 0.892601i \(-0.648878\pi\)
−0.450847 + 0.892601i \(0.648878\pi\)
\(510\) −11.3137 + 5.65685i −0.500979 + 0.250490i
\(511\) 32.9706 1.45853
\(512\) 31.2426i 1.38074i
\(513\) 4.00000i 0.176604i
\(514\) −24.4853 −1.08000
\(515\) −31.3137 + 15.6569i −1.37985 + 0.689923i
\(516\) 36.9706 1.62754
\(517\) 0.343146i 0.0150915i
\(518\) 98.9117i 4.34593i
\(519\) 8.97056 0.393764
\(520\) 5.17157 + 10.3431i 0.226788 + 0.453577i
\(521\) −14.0000 −0.613351 −0.306676 0.951814i \(-0.599217\pi\)
−0.306676 + 0.951814i \(0.599217\pi\)
\(522\) 2.00000i 0.0875376i
\(523\) 26.9706i 1.17934i −0.807644 0.589670i \(-0.799258\pi\)
0.807644 0.589670i \(-0.200742\pi\)
\(524\) 58.6274 2.56115
\(525\) −28.9706 + 38.6274i −1.26438 + 1.68584i
\(526\) −3.65685 −0.159446
\(527\) 1.37258i 0.0597907i
\(528\) 6.00000i 0.261116i
\(529\) 9.62742 0.418583
\(530\) −12.4853 24.9706i −0.542326 1.08465i
\(531\) 2.82843 0.122743
\(532\) 18.4853i 0.801439i
\(533\) 12.2843i 0.532091i
\(534\) 75.5980 3.27144
\(535\) 29.9411 14.9706i 1.29447 0.647234i
\(536\) 26.4853 1.14399
\(537\) 0.970563i 0.0418829i
\(538\) 26.4853i 1.14186i
\(539\) 16.3137 0.702681
\(540\) −30.6274 + 15.3137i −1.31799 + 0.658997i
\(541\) −23.6569 −1.01709 −0.508544 0.861036i \(-0.669816\pi\)
−0.508544 + 0.861036i \(0.669816\pi\)
\(542\) 27.3137i 1.17322i
\(543\) 28.0000i 1.20160i
\(544\) 1.85786 0.0796553
\(545\) −4.82843 9.65685i −0.206827 0.413654i
\(546\) 27.3137 1.16892
\(547\) 22.2843i 0.952807i −0.879227 0.476403i \(-0.841940\pi\)
0.879227 0.476403i \(-0.158060\pi\)
\(548\) 30.6274i 1.30834i
\(549\) 2.00000 0.0853579
\(550\) −9.65685 7.24264i −0.411770 0.308827i
\(551\) −0.828427 −0.0352922
\(552\) 32.2843i 1.37411i
\(553\) 27.3137i 1.16150i
\(554\) 31.7990 1.35101
\(555\) −16.9706 33.9411i −0.720360 1.44072i
\(556\) 15.3137 0.649446
\(557\) 39.1127i 1.65726i 0.559798 + 0.828629i \(0.310879\pi\)
−0.559798 + 0.828629i \(0.689121\pi\)
\(558\) 2.82843i 0.119737i
\(559\) −5.65685 −0.239259
\(560\) −28.9706 + 14.4853i −1.22423 + 0.612115i
\(561\) −2.34315 −0.0989277
\(562\) 75.9411i 3.20338i
\(563\) 14.9706i 0.630934i 0.948937 + 0.315467i \(0.102161\pi\)
−0.948937 + 0.315467i \(0.897839\pi\)
\(564\) −2.62742 −0.110634
\(565\) −36.2843 + 18.1421i −1.52649 + 0.763245i
\(566\) 25.3137 1.06401
\(567\) 53.1127i 2.23052i
\(568\) 40.4853i 1.69872i
\(569\) 27.1716 1.13909 0.569546 0.821960i \(-0.307119\pi\)
0.569546 + 0.821960i \(0.307119\pi\)
\(570\) −4.82843 9.65685i −0.202241 0.404481i
\(571\) 32.2843 1.35105 0.675527 0.737335i \(-0.263916\pi\)
0.675527 + 0.737335i \(0.263916\pi\)
\(572\) 4.48528i 0.187539i
\(573\) 33.9411i 1.41791i
\(574\) 122.225 5.10159
\(575\) 14.6274 + 10.9706i 0.610005 + 0.457504i
\(576\) −9.82843 −0.409518
\(577\) 32.0000i 1.33218i −0.745873 0.666089i \(-0.767967\pi\)
0.745873 0.666089i \(-0.232033\pi\)
\(578\) 37.7279i 1.56927i
\(579\) −28.2843 −1.17545
\(580\) −3.17157 6.34315i −0.131692 0.263385i
\(581\) 50.6274 2.10038
\(582\) 32.9706i 1.36667i
\(583\) 5.17157i 0.214185i
\(584\) −30.1421 −1.24729
\(585\) −2.34315 + 1.17157i −0.0968772 + 0.0484386i
\(586\) 5.17157 0.213636
\(587\) 34.2843i 1.41506i 0.706682 + 0.707532i \(0.250191\pi\)
−0.706682 + 0.707532i \(0.749809\pi\)
\(588\) 124.912i 5.15127i
\(589\) −1.17157 −0.0482738
\(590\) 13.6569 6.82843i 0.562244 0.281122i
\(591\) 44.2843 1.82161
\(592\) 25.4558i 1.04623i
\(593\) 45.4558i 1.86665i 0.359036 + 0.933324i \(0.383106\pi\)
−0.359036 + 0.933324i \(0.616894\pi\)
\(594\) −9.65685 −0.396226
\(595\) 5.65685 + 11.3137i 0.231908 + 0.463817i
\(596\) −75.2548 −3.08256
\(597\) 11.3137i 0.463039i
\(598\) 10.3431i 0.422963i
\(599\) −25.1716 −1.02848 −0.514241 0.857646i \(-0.671926\pi\)
−0.514241 + 0.857646i \(0.671926\pi\)
\(600\) 26.4853 35.3137i 1.08126 1.44168i
\(601\) 37.1127 1.51386 0.756929 0.653497i \(-0.226699\pi\)
0.756929 + 0.653497i \(0.226699\pi\)
\(602\) 56.2843i 2.29398i
\(603\) 6.00000i 0.244339i
\(604\) −82.9117 −3.37363
\(605\) −1.00000 2.00000i −0.0406558 0.0813116i
\(606\) −64.2843 −2.61137
\(607\) 39.6569i 1.60962i 0.593531 + 0.804811i \(0.297733\pi\)
−0.593531 + 0.804811i \(0.702267\pi\)
\(608\) 1.58579i 0.0643121i
\(609\) −8.00000 −0.324176
\(610\) 9.65685 4.82843i 0.390995 0.195497i
\(611\) 0.402020 0.0162640
\(612\) 4.48528i 0.181307i
\(613\) 18.8284i 0.760473i −0.924889 0.380237i \(-0.875843\pi\)
0.924889 0.380237i \(-0.124157\pi\)
\(614\) 16.8284 0.679140
\(615\) −41.9411 + 20.9706i −1.69123 + 0.845615i
\(616\) −21.3137 −0.858754
\(617\) 10.3431i 0.416399i −0.978086 0.208200i \(-0.933240\pi\)
0.978086 0.208200i \(-0.0667604\pi\)
\(618\) 75.5980i 3.04100i
\(619\) −18.6274 −0.748699 −0.374350 0.927288i \(-0.622134\pi\)
−0.374350 + 0.927288i \(0.622134\pi\)
\(620\) −4.48528 8.97056i −0.180133 0.360266i
\(621\) 14.6274 0.586978
\(622\) 79.5980i 3.19159i
\(623\) 75.5980i 3.02877i
\(624\) −7.02944 −0.281403
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) −40.9706 −1.63751
\(627\) 2.00000i 0.0798723i
\(628\) 45.9411i 1.83325i
\(629\) −9.94113 −0.396379
\(630\) −11.6569 23.3137i −0.464420 0.928840i
\(631\) −0.970563 −0.0386375 −0.0193187 0.999813i \(-0.506150\pi\)
−0.0193187 + 0.999813i \(0.506150\pi\)
\(632\) 24.9706i 0.993276i
\(633\) 14.6274i 0.581388i
\(634\) −53.4558 −2.12300
\(635\) −28.0000 + 14.0000i −1.11115 + 0.555573i
\(636\) 39.5980 1.57016
\(637\) 19.1127i 0.757273i
\(638\) 2.00000i 0.0791808i
\(639\) 9.17157 0.362822
\(640\) −41.1127 + 20.5563i −1.62512 + 0.812561i
\(641\) −3.65685 −0.144437 −0.0722185 0.997389i \(-0.523008\pi\)
−0.0722185 + 0.997389i \(0.523008\pi\)
\(642\) 72.2843i 2.85283i
\(643\) 19.9411i 0.786401i −0.919453 0.393201i \(-0.871368\pi\)
0.919453 0.393201i \(-0.128632\pi\)
\(644\) 67.5980 2.66373
\(645\) 9.65685 + 19.3137i 0.380238 + 0.760477i
\(646\) −2.82843 −0.111283
\(647\) 25.3137i 0.995185i −0.867411 0.497592i \(-0.834218\pi\)
0.867411 0.497592i \(-0.165782\pi\)
\(648\) 48.5563i 1.90747i
\(649\) 2.82843 0.111025
\(650\) −8.48528 + 11.3137i −0.332820 + 0.443760i
\(651\) −11.3137 −0.443419
\(652\) 7.65685i 0.299866i
\(653\) 10.6274i 0.415883i 0.978141 + 0.207941i \(0.0666764\pi\)
−0.978141 + 0.207941i \(0.933324\pi\)
\(654\) 23.3137 0.911638
\(655\) 15.3137 + 30.6274i 0.598356 + 1.19671i
\(656\) −31.4558 −1.22814
\(657\) 6.82843i 0.266402i
\(658\) 4.00000i 0.155936i
\(659\) 18.6274 0.725621 0.362811 0.931863i \(-0.381817\pi\)
0.362811 + 0.931863i \(0.381817\pi\)
\(660\) 15.3137 7.65685i 0.596085 0.298043i
\(661\) 17.3137 0.673425 0.336713 0.941607i \(-0.390685\pi\)
0.336713 + 0.941607i \(0.390685\pi\)
\(662\) 53.4558i 2.07762i
\(663\) 2.74517i 0.106613i
\(664\) −46.2843 −1.79618
\(665\) −9.65685 + 4.82843i −0.374477 + 0.187238i
\(666\) 20.4853 0.793789
\(667\) 3.02944i 0.117300i
\(668\) 75.2548i 2.91170i
\(669\) −0.686292 −0.0265336
\(670\) 14.4853 + 28.9706i 0.559615 + 1.11923i
\(671\) 2.00000 0.0772091
\(672\) 15.3137i 0.590739i
\(673\) 6.14214i 0.236762i −0.992968 0.118381i \(-0.962230\pi\)
0.992968 0.118381i \(-0.0377704\pi\)
\(674\) 6.82843 0.263021
\(675\) −16.0000 12.0000i −0.615840 0.461880i
\(676\) −44.5147 −1.71210
\(677\) 36.4853i 1.40224i −0.713042 0.701122i \(-0.752683\pi\)
0.713042 0.701122i \(-0.247317\pi\)
\(678\) 87.5980i 3.36418i
\(679\) −32.9706 −1.26529
\(680\) −5.17157 10.3431i −0.198321 0.396642i
\(681\) 47.3137 1.81307
\(682\) 2.82843i 0.108306i
\(683\) 28.6274i 1.09540i −0.836676 0.547699i \(-0.815504\pi\)
0.836676 0.547699i \(-0.184496\pi\)
\(684\) 3.82843 0.146384
\(685\) −16.0000 + 8.00000i −0.611329 + 0.305664i
\(686\) 108.569 4.14517
\(687\) 44.0000i 1.67870i
\(688\) 14.4853i 0.552246i
\(689\) −6.05887 −0.230825
\(690\) −35.3137 + 17.6569i −1.34437 + 0.672185i
\(691\) −28.0000 −1.06517 −0.532585 0.846376i \(-0.678779\pi\)
−0.532585 + 0.846376i \(0.678779\pi\)
\(692\) 17.1716i 0.652765i
\(693\) 4.82843i 0.183417i
\(694\) −46.2843 −1.75693
\(695\) 4.00000 + 8.00000i 0.151729 + 0.303457i
\(696\) 7.31371 0.277225
\(697\) 12.2843i 0.465300i
\(698\) 39.4558i 1.49343i
\(699\) −24.9706 −0.944473
\(700\) −73.9411 55.4558i −2.79471 2.09603i
\(701\) −22.2843 −0.841665 −0.420833 0.907138i \(-0.638262\pi\)
−0.420833 + 0.907138i \(0.638262\pi\)
\(702\) 11.3137i 0.427008i
\(703\) 8.48528i 0.320028i
\(704\) −9.82843 −0.370423
\(705\) −0.686292 1.37258i −0.0258472 0.0516945i
\(706\) 0 0
\(707\) 64.2843i 2.41766i
\(708\) 21.6569i 0.813914i
\(709\) −29.3137 −1.10090 −0.550450 0.834868i \(-0.685544\pi\)
−0.550450 + 0.834868i \(0.685544\pi\)
\(710\) 44.2843 22.1421i 1.66196 0.830980i
\(711\) −5.65685 −0.212149
\(712\) 69.1127i 2.59011i
\(713\) 4.28427i 0.160447i
\(714\) −27.3137 −1.02219
\(715\) −2.34315 + 1.17157i −0.0876287 + 0.0438143i
\(716\) −1.85786 −0.0694317
\(717\) 54.6274i 2.04010i
\(718\) 40.9706i 1.52901i
\(719\) 30.6274 1.14221 0.571105 0.820877i \(-0.306515\pi\)
0.571105 + 0.820877i \(0.306515\pi\)
\(720\) 3.00000 + 6.00000i 0.111803 + 0.223607i
\(721\) −75.5980 −2.81542
\(722\) 2.41421i 0.0898477i
\(723\) 20.9706i 0.779904i
\(724\) −53.5980 −1.99195
\(725\) 2.48528 3.31371i 0.0923010 0.123068i
\(726\) 4.82843 0.179200
\(727\) 9.31371i 0.345426i −0.984972 0.172713i \(-0.944747\pi\)
0.984972 0.172713i \(-0.0552534\pi\)
\(728\) 24.9706i 0.925471i
\(729\) −13.0000 −0.481481
\(730\) −16.4853 32.9706i −0.610148 1.22030i
\(731\) 5.65685 0.209226
\(732\) 15.3137i 0.566011i
\(733\) 8.48528i 0.313411i 0.987645 + 0.156706i \(0.0500874\pi\)
−0.987645 + 0.156706i \(0.949913\pi\)
\(734\) 76.4264 2.82095
\(735\) −65.2548 + 32.6274i −2.40696 + 1.20348i
\(736\) 5.79899 0.213754
\(737\) 6.00000i 0.221013i
\(738\) 25.3137i 0.931810i
\(739\) 44.0000 1.61857 0.809283 0.587419i \(-0.199856\pi\)
0.809283 + 0.587419i \(0.199856\pi\)
\(740\) 64.9706 32.4853i 2.38837 1.19418i
\(741\) −2.34315 −0.0860776
\(742\) 60.2843i 2.21311i
\(743\) 22.9706i 0.842708i −0.906896 0.421354i \(-0.861555\pi\)
0.906896 0.421354i \(-0.138445\pi\)
\(744\) 10.3431 0.379198
\(745\) −19.6569 39.3137i −0.720171 1.44034i
\(746\) −55.1127 −2.01782
\(747\) 10.4853i 0.383636i
\(748\) 4.48528i 0.163998i
\(749\) 72.2843 2.64121
\(750\) 53.1127 + 9.65685i 1.93940 + 0.352618i
\(751\) 19.5147 0.712102 0.356051 0.934466i \(-0.384123\pi\)
0.356051 + 0.934466i \(0.384123\pi\)
\(752\) 1.02944i 0.0375397i
\(753\) 8.00000i 0.291536i
\(754\) −2.34315 −0.0853323
\(755\) −21.6569 43.3137i −0.788174 1.57635i
\(756\) −73.9411 −2.68921
\(757\) 20.0000i 0.726912i −0.931611 0.363456i \(-0.881597\pi\)
0.931611 0.363456i \(-0.118403\pi\)
\(758\) 12.4853i 0.453486i
\(759\) −7.31371 −0.265471
\(760\) 8.82843 4.41421i 0.320241 0.160120i
\(761\) 19.9411 0.722865 0.361433 0.932398i \(-0.382288\pi\)
0.361433 + 0.932398i \(0.382288\pi\)
\(762\) 67.5980i 2.44882i
\(763\) 23.3137i 0.844013i
\(764\) 64.9706 2.35055
\(765\) 2.34315 1.17157i 0.0847166 0.0423583i
\(766\) 16.8284 0.608036
\(767\) 3.31371i 0.119651i
\(768\) 59.9411i 2.16294i
\(769\) −19.6569 −0.708844 −0.354422 0.935086i \(-0.615322\pi\)
−0.354422 + 0.935086i \(0.615322\pi\)
\(770\) −11.6569 23.3137i −0.420084 0.840168i
\(771\) 20.2843 0.730520
\(772\) 54.1421i 1.94862i
\(773\) 10.8284i 0.389471i −0.980856 0.194736i \(-0.937615\pi\)
0.980856 0.194736i \(-0.0623849\pi\)
\(774\) −11.6569 −0.418997
\(775\) 3.51472 4.68629i 0.126252 0.168337i
\(776\) 30.1421 1.08204
\(777\) 81.9411i 2.93962i
\(778\) 22.4853i 0.806136i
\(779\) −10.4853 −0.375674
\(780\) −8.97056 17.9411i −0.321198 0.642395i
\(781\) 9.17157 0.328185
\(782\) 10.3431i 0.369870i
\(783\) 3.31371i 0.118422i
\(784\) −48.9411 −1.74790
\(785\) −24.0000 + 12.0000i −0.856597 + 0.428298i
\(786\) −73.9411 −2.63739
\(787\) 30.9706i 1.10398i 0.833850 + 0.551991i \(0.186132\pi\)
−0.833850 + 0.551991i \(0.813868\pi\)
\(788\) 84.7696i 3.01979i
\(789\) 3.02944 0.107851
\(790\) −27.3137 + 13.6569i −0.971778 + 0.485889i
\(791\) −87.5980 −3.11463
\(792\) 4.41421i 0.156852i
\(793\) 2.34315i 0.0832075i
\(794\) 36.9706 1.31204
\(795\) 10.3431 + 20.6863i 0.366834 + 0.733667i
\(796\) 21.6569 0.767607
\(797\) 5.17157i 0.183187i 0.995797 + 0.0915933i \(0.0291960\pi\)
−0.995797 + 0.0915933i \(0.970804\pi\)
\(798\) 23.3137i 0.825296i
\(799\) −0.402020 −0.0142225
\(800\) −6.34315 4.75736i −0.224264 0.168198i
\(801\) −15.6569 −0.553208
\(802\) 41.7990i 1.47597i
\(803\) 6.82843i 0.240970i
\(804\) −45.9411 −1.62022
\(805\) 17.6569 + 35.3137i 0.622322 + 1.24464i
\(806\) −3.31371 −0.116720
\(807\) 21.9411i 0.772364i
\(808\) 58.7696i 2.06751i
\(809\) 30.6863 1.07887 0.539436 0.842026i \(-0.318637\pi\)
0.539436 + 0.842026i \(0.318637\pi\)
\(810\) 53.1127 26.5563i 1.86619 0.933095i
\(811\) 40.2843 1.41457 0.707286 0.706927i \(-0.249919\pi\)
0.707286 + 0.706927i \(0.249919\pi\)
\(812\) 15.3137i 0.537406i
\(813\) 22.6274i 0.793578i
\(814\) 20.4853 0.718009
\(815\) −4.00000 + 2.00000i −0.140114 + 0.0700569i
\(816\) 7.02944 0.246080
\(817\) 4.82843i 0.168925i
\(818\) 46.2843i 1.61829i
\(819\) −5.65685 −0.197666
\(820\) −40.1421 80.2843i −1.40182 2.80365i
\(821\) 15.9411 0.556349 0.278175 0.960531i \(-0.410271\pi\)
0.278175 + 0.960531i \(0.410271\pi\)
\(822\) 38.6274i 1.34729i
\(823\) 13.3137i 0.464087i 0.972705 + 0.232043i \(0.0745411\pi\)
−0.972705 + 0.232043i \(0.925459\pi\)
\(824\) 69.1127 2.40765
\(825\) 8.00000 + 6.00000i 0.278524 + 0.208893i
\(826\) 32.9706 1.14719
\(827\) 37.3137i 1.29752i −0.760991 0.648762i \(-0.775287\pi\)
0.760991 0.648762i \(-0.224713\pi\)
\(828\) 14.0000i 0.486534i
\(829\) 48.9117 1.69877 0.849387 0.527771i \(-0.176972\pi\)
0.849387 + 0.527771i \(0.176972\pi\)
\(830\) −25.3137 50.6274i −0.878652 1.75730i
\(831\) −26.3431 −0.913834
\(832\) 11.5147i 0.399201i
\(833\) 19.1127i 0.662216i
\(834\) −19.3137 −0.668779
\(835\) −39.3137 + 19.6569i −1.36051 + 0.680253i
\(836\) 3.82843 0.132409
\(837\) 4.68629i 0.161982i
\(838\) 31.3137i 1.08171i
\(839\) 31.7990 1.09782 0.548912 0.835880i \(-0.315042\pi\)
0.548912 + 0.835880i \(0.315042\pi\)
\(840\) 85.2548 42.6274i 2.94157 1.47079i
\(841\) −28.3137 −0.976335
\(842\) 16.8284i 0.579946i
\(843\) 62.9117i 2.16679i
\(844\) 28.0000 0.963800
\(845\) −11.6274 23.2548i −0.399995 0.799991i
\(846\) 0.828427 0.0284819
\(847\) 4.82843i 0.165907i
\(848\) 15.5147i 0.532778i
\(849\) −20.9706 −0.719708
\(850\) 8.48528 11.3137i 0.291043 0.388057i
\(851\) −31.0294 −1.06368
\(852\) 70.2254i 2.40588i
\(853\) 39.5147i 1.35296i 0.736462 + 0.676479i \(0.236495\pi\)
−0.736462 + 0.676479i \(0.763505\pi\)
\(854\) 23.3137 0.797779
\(855\) 1.00000 + 2.00000i 0.0341993 + 0.0683986i
\(856\) −66.0833 −2.25868
\(857\) 48.0833i 1.64249i 0.570574 + 0.821246i \(0.306721\pi\)
−0.570574 + 0.821246i \(0.693279\pi\)
\(858\) 5.65685i 0.193122i
\(859\) 24.6863 0.842285 0.421143 0.906994i \(-0.361629\pi\)
0.421143 + 0.906994i \(0.361629\pi\)
\(860\) −36.9706 + 18.4853i −1.26069 + 0.630343i
\(861\) −101.255 −3.45076
\(862\) 93.2548i 3.17627i
\(863\) 9.02944i 0.307366i −0.988120 0.153683i \(-0.950887\pi\)
0.988120 0.153683i \(-0.0491134\pi\)
\(864\) −6.34315 −0.215798
\(865\) −8.97056 + 4.48528i −0.305008 + 0.152504i
\(866\) 16.4853 0.560193
\(867\) 31.2548i 1.06147i
\(868\) 21.6569i 0.735082i
\(869\) −5.65685 −0.191896
\(870\) 4.00000 + 8.00000i 0.135613 + 0.271225i
\(871\) 7.02944 0.238183
\(872\) 21.3137i 0.721773i
\(873\) 6.82843i 0.231107i
\(874\) −8.82843 −0.298626
\(875\) 9.65685 53.1127i 0.326461 1.79554i
\(876\) 52.2843 1.76652
\(877\) 26.1421i 0.882757i −0.897321 0.441379i \(-0.854490\pi\)
0.897321 0.441379i \(-0.145510\pi\)
\(878\) 71.5980i 2.41631i
\(879\) −4.28427 −0.144505
\(880\) 3.00000 + 6.00000i 0.101130 + 0.202260i
\(881\) 35.9411 1.21089 0.605444 0.795888i \(-0.292996\pi\)
0.605444 + 0.795888i \(0.292996\pi\)
\(882\) 39.3848i 1.32615i
\(883\) 10.6863i 0.359622i 0.983701 + 0.179811i \(0.0575487\pi\)
−0.983701 + 0.179811i \(0.942451\pi\)
\(884\) −5.25483 −0.176739
\(885\) −11.3137 + 5.65685i −0.380306 + 0.190153i
\(886\) −32.1421 −1.07984
\(887\) 51.9411i 1.74401i 0.489495 + 0.872006i \(0.337181\pi\)
−0.489495 + 0.872006i \(0.662819\pi\)
\(888\) 74.9117i 2.51387i
\(889\) −67.5980 −2.26716
\(890\) −75.5980 + 37.7990i −2.53405 + 1.26703i
\(891\) 11.0000 0.368514
\(892\) 1.31371i 0.0439862i
\(893\) 0.343146i 0.0114829i
\(894\) 94.9117 3.17432
\(895\) −0.485281 0.970563i −0.0162212 0.0324423i
\(896\) −99.2548 −3.31587
\(897\) 8.56854i 0.286095i
\(898\) 74.7696i 2.49509i
\(899\) 0.970563 0.0323701
\(900\) −11.4853 + 15.3137i −0.382843 + 0.510457i
\(901\) 6.05887 0.201850
\(902\) 25.3137i 0.842854i
\(903\) 46.6274i 1.55166i
\(904\) 80.0833 2.66353
\(905\) −14.0000 28.0000i −0.465376 0.930751i
\(906\) 104.569 3.47406
\(907\) 16.6274i 0.552104i 0.961143 + 0.276052i \(0.0890263\pi\)
−0.961143 + 0.276052i \(0.910974\pi\)
\(908\) 90.5685i 3.00562i
\(909\) 13.3137 0.441588
\(910\) −27.3137 + 13.6569i −0.905441 + 0.452720i
\(911\) 30.8284 1.02139 0.510696 0.859762i \(-0.329388\pi\)
0.510696 + 0.859762i \(0.329388\pi\)
\(912\) 6.00000i 0.198680i
\(913\) 10.4853i 0.347012i
\(914\) −57.4558 −1.90047
\(915\) −8.00000 + 4.00000i −0.264472 + 0.132236i
\(916\) −84.2254 −2.78289
\(917\) 73.9411i 2.44175i
\(918\) 11.3137i 0.373408i
\(919\) 15.0294 0.495775 0.247888 0.968789i \(-0.420264\pi\)
0.247888 + 0.968789i \(0.420264\pi\)
\(920\) −16.1421 32.2843i −0.532190 1.06438i
\(921\) −13.9411 −0.459376
\(922\) 82.7696i 2.72587i
\(923\) 10.7452i 0.353681i
\(924\) 36.9706 1.21624
\(925\) 33.9411 + 25.4558i 1.11598 + 0.836983i
\(926\) −63.4558 −2.08529
\(927\) 15.6569i 0.514239i
\(928\) 1.31371i 0.0431246i
\(929\) 11.9411 0.391776 0.195888 0.980626i \(-0.437241\pi\)
0.195888 + 0.980626i \(0.437241\pi\)
\(930\) 5.65685 + 11.3137i 0.185496 + 0.370991i
\(931\) −16.3137 −0.534660
\(932\) 47.7990i 1.56571i
\(933\) 65.9411i 2.15882i
\(934\) −37.7990 −1.23682
\(935\) 2.34315 1.17157i 0.0766291 0.0383145i
\(936\) 5.17157 0.169038
\(937\) 43.1127i 1.40843i −0.709987 0.704215i \(-0.751299\pi\)
0.709987 0.704215i \(-0.248701\pi\)
\(938\) 69.9411i 2.28366i
\(939\) 33.9411 1.10763
\(940\) 2.62742 1.31371i 0.0856969 0.0428484i
\(941\) −52.1421 −1.69979 −0.849893 0.526956i \(-0.823333\pi\)
−0.849893 + 0.526956i \(0.823333\pi\)
\(942\) 57.9411i 1.88782i
\(943\) 38.3431i 1.24862i
\(944\) −8.48528 −0.276172
\(945\) −19.3137 38.6274i −0.628275 1.25655i
\(946\) −11.6569 −0.378997
\(947\) 1.71573i 0.0557537i 0.999611 + 0.0278768i \(0.00887463\pi\)
−0.999611 + 0.0278768i \(0.991125\pi\)
\(948\) 43.3137i 1.40676i
\(949\) −8.00000 −0.259691
\(950\) 9.65685 + 7.24264i 0.313310 + 0.234982i
\(951\) 44.2843 1.43602
\(952\) 24.9706i 0.809301i
\(953\) 23.1127i 0.748694i −0.927289 0.374347i \(-0.877867\pi\)
0.927289 0.374347i \(-0.122133\pi\)
\(954\) −12.4853 −0.404226
\(955\) 16.9706 + 33.9411i 0.549155 + 1.09831i
\(956\) 104.569 3.38199
\(957\) 1.65685i 0.0535585i
\(958\) 46.6274i 1.50646i
\(959\) −38.6274 −1.24734
\(960\) 39.3137 19.6569i 1.26884 0.634422i
\(961\) −29.6274 −0.955723
\(962\) 24.0000i 0.773791i
\(963\) 14.9706i 0.482420i
\(964\) 40.1421 1.29289
\(965\) 28.2843 14.1421i 0.910503 0.455251i
\(966\) −85.2548 −2.74303
\(967\) 16.1421i 0.519096i −0.965730 0.259548i \(-0.916426\pi\)
0.965730 0.259548i \(-0.0835736\pi\)
\(968\) 4.41421i 0.141878i
\(969\) 2.34315 0.0752727
\(970\) 16.4853 + 32.9706i 0.529310 + 1.05862i
\(971\) 47.1127 1.51192 0.755959 0.654619i \(-0.227171\pi\)
0.755959 + 0.654619i \(0.227171\pi\)
\(972\) 38.2843i 1.22797i
\(973\) 19.3137i 0.619169i
\(974\) −10.4853 −0.335970
\(975\) 7.02944 9.37258i 0.225122 0.300163i
\(976\) −6.00000 −0.192055
\(977\) 31.7990i 1.01734i −0.860962 0.508670i \(-0.830137\pi\)
0.860962 0.508670i \(-0.169863\pi\)
\(978\) 9.65685i 0.308792i
\(979\) −15.6569 −0.500395
\(980\) −62.4558 124.912i −1.99508 3.99016i
\(981\) −4.82843 −0.154160
\(982\) 7.31371i 0.233390i
\(983\) 19.6569i 0.626956i 0.949595 + 0.313478i \(0.101494\pi\)
−0.949595 + 0.313478i \(0.898506\pi\)
\(984\) 92.5685 2.95098
\(985\) −44.2843 + 22.1421i −1.41101 + 0.705507i
\(986\) 2.34315 0.0746210
\(987\) 3.31371i 0.105477i
\(988\) 4.48528i 0.142696i
\(989\) 17.6569 0.561455
\(990\) −4.82843 + 2.41421i −0.153457 + 0.0767287i
\(991\) 17.1716 0.545473 0.272736 0.962089i \(-0.412071\pi\)
0.272736 + 0.962089i \(0.412071\pi\)
\(992\) 1.85786i 0.0589873i
\(993\) 44.2843i 1.40532i
\(994\) 106.912 3.39103
\(995\) 5.65685 + 11.3137i 0.179334 + 0.358669i
\(996\) 80.2843 2.54390
\(997\) 0.485281i 0.0153690i −0.999970 0.00768451i \(-0.997554\pi\)
0.999970 0.00768451i \(-0.00244608\pi\)
\(998\) 56.2843i 1.78165i
\(999\) 33.9411 1.07385
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1045.2.b.a.419.1 4
5.2 odd 4 5225.2.a.g.1.2 2
5.3 odd 4 5225.2.a.d.1.1 2
5.4 even 2 inner 1045.2.b.a.419.4 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1045.2.b.a.419.1 4 1.1 even 1 trivial
1045.2.b.a.419.4 yes 4 5.4 even 2 inner
5225.2.a.d.1.1 2 5.3 odd 4
5225.2.a.g.1.2 2 5.2 odd 4